#### Study sets matching "conics"

#### Study sets matching "conics"

What is the Directrix ?

What is the Focus of a parabola?

Equation of Parabola in Standard Form

Equation of Parabola in Vertex Form

A fixed line that defines the parabola. Every point on the pa…

What is the Directrix ?

A fixed line that defines the parabola. Every point on the pa…

What is the Focus of a parabola?

how know if equation is a circle

how know if equation is a parabola

how know if equation is an elipse

how know if equation is a hyperbola

2 squared terms

1 squared term

2 squared terms = 1

2 squared terms and (-) sign

how know if equation is a circle

2 squared terms

how know if equation is a parabola

1 squared term

Center of a Circle

Circle

Conic Section

Diameter

The point inside the circle that is the same distance from al…

The set of all points in a plane that are the same distance,…

A figure formed by the intersection of a plane and a right ci…

The distance across a circle through its center. The line seg…

Center of a Circle

The point inside the circle that is the same distance from al…

Circle

The set of all points in a plane that are the same distance,…

What is the Directrix ?

What is the Focus of a parabola?

Equation of Parabola in Standard Form

Equation of Parabola in Vertex Form

A fixed line that defines the parabola. Every point on the pa…

What is the Directrix ?

A fixed line that defines the parabola. Every point on the pa…

What is the Focus of a parabola?

Ellipse

Hyperbolas

Hyperbola Standard Form

Circle Standard Form

A set of points where the distance form any point (x,y) on th…

The set of all points that have the following characteristics…

Ellipse

A set of points where the distance form any point (x,y) on th…

Hyperbolas

The set of all points that have the following characteristics…

Axis

Branch

Center

Circle

The line over which a parabola is symmetric.

The term for each of the two distinct sections of the graph o…

For an ellipse and hyperbola, the midpoint between the foci.…

The set of all points equidistant from a given fixed point.

Axis

The line over which a parabola is symmetric.

Branch

The term for each of the two distinct sections of the graph o…

Form of an Equation:... y = a(x-h)^2 + k…

Form of an Equation:... x = a(y-k)^2 + h…

Vertex

Axis of Symmetry

Up if a > 0, down if a < 0

Right if a > 0, Left if a < 0

Always (h,k)

x=h in up/down parabola & y=k in right/left parabola

Form of an Equation:... y = a(x-h)^2 + k…

Up if a > 0, down if a < 0

Form of an Equation:... x = a(y-k)^2 + h…

Right if a > 0, Left if a < 0

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1

(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

(y - k)^2 / a^2 - (x - h)^2 / b^2 = 1

Ellipse (left to right)

Ellipse (up and down)

Hyperbola (left and right sides)

Hyperbola ( top and bottom)

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

Ellipse (left to right)

(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1

Ellipse (up and down)

Circle

radius

Standard form of a circle

Center of circle

the set of all points in a plane that are equidistant from a…

the distance from the center to any point on the circle

(x-h)^2+(y-k)^2=r^2... or ... x^2+y^2=r^2

(h,k)

Circle

the set of all points in a plane that are equidistant from a…

radius

the distance from the center to any point on the circle

distance formula

midpoint formula

standard form for a circle

domain and range of a circle

used to find diameter or radius when given 2 sets of points

used to find the center

x^2 + y^2 = r^2 OR (x-h)^2 + (y-k)^2 = r^2... x and y coefficie…

[brackets], domain - left to right, range - bottom to top

distance formula

used to find diameter or radius when given 2 sets of points

midpoint formula

used to find the center

Parabola

Ellipse

Hyperbola

Asymptote of hyperbolas when y is first

The set of all points in a plane that are equidistant from a…

Set of all points on a plane, the sum of whose distances from…

Set of all points in a plane, the difference of whose distanc…

y=k +/- a/b (x-h)

Parabola

The set of all points in a plane that are equidistant from a…

Ellipse

Set of all points on a plane, the sum of whose distances from…

locus

circle

ellipse

hyperbola

set of points that satisfy a given rule

a locus of points in a plane at a fixed distances,r, from a g…

locus of points in a plane for which the sum of the distances…

a locus of points in a plane for which the difference of the…

locus

set of points that satisfy a given rule

circle

a locus of points in a plane at a fixed distances,r, from a g…

circle

parabola

ellipse

hyperbola

coefficients same, both squared INCLUDING the sign

only one variable squared NOT both

when x and y are both squared and the coefficients are positi…

x and y are both squared and diff. signs

circle

coefficients same, both squared INCLUDING the sign

parabola

only one variable squared NOT both

Parabolas (horizontal, open side to si…

Parabolas (vertical, open up and down)

Ellipse (horizontally long)

Ellipse (vertically long)

(y-k)^2 = 4p(x-h)

(x-h)^2 = 4p(y-k)

(x-h)^2 / a^2 + (y-k)^2 / b^2 =1

(x-h)^2 / b^2 + (y-k)^2 / a^2 =1

Parabolas (horizontal, open side to si…

(y-k)^2 = 4p(x-h)

Parabolas (vertical, open up and down)

(x-h)^2 = 4p(y-k)

circle

Circle

center

radius

the intersection of a right circular cone with a plane that i…

the set of all points in a plane that are fixed distance from…

fixed point that is the same distance from all points on the…

segment whose endpoints are the center of the circle and a po…

circle

the intersection of a right circular cone with a plane that i…

Circle

the set of all points in a plane that are fixed distance from…